Exhibit 12-10
The following information regarding a dependent variable Y and an independent variable X is provided.
$$\begin{array} { l }
\mathrm { n } = 4 \
\Sigma \mathrm { X } = 16 \
\Sigma \mathrm { Y } = 28 \
\Sigma \mathrm { Y } - { \bar { Y )} } \mathrm { X } - \bar { X } ) = - 8 \
\Sigma \mathrm { X } - \bar { X } ) ^ { 2 } = 8 \
\mathrm { SST } = 42 \
\mathrm { SSE } = 34
\end{array}$$
-Refer to Exhibit 12-10. The coefficient of correlation is
A) 0.1905
B) -0.1905
C) 0.4364
D) -0.4364

Question

Exhibit 12-10
The following information regarding a dependent variable Y and an independent variable X is provided.
 $$\begin{array} { l } 
\mathrm { n } = 4 \
\Sigma \mathrm { X } = 16 \
\Sigma \mathrm { Y } = 28 \
\Sigma \mathrm { Y } - { \bar { Y )} } \mathrm { X } - \bar { X } ) = - 8 \
\Sigma \mathrm { X } - \bar { X } ) ^ { 2 } = 8 \
\mathrm { SST } = 42 \
\mathrm { SSE } = 34
\end{array}$$
-Refer to Exhibit 12-10. The coefficient of correlation is
A) 0.1905
B) -0.1905
C) 0.4364
D) -0.4364

Quizplus · Accepted Answer

The coefficient of correlation (r) is calculated as the square root of the coefficient of determination (R²), which is 1 - (SSE/SST). Here, R² = 1 - (34/42) = 0.1905. Since the sum of (Y - Ȳ)(X - X̄) is negative, r is negative, so r = -√0.1905 = -0.4364.

Exhibit 12-10 the Following Information Regarding a Dependent Variable Y

Exhibit 12-10
the Following Information Regarding a Dependent Variable Y